Theorems · Theorem · geometry

AffineEquiv.apply_lineMap

∀ {k : Type u_1} {P₁ : Type u_2} {P₂ : Type u_3} {V₁ : Type u_6} {V₂ : Type u_7} [inst : Ring k]
  [inst_1 : AddCommGroup V₁] [inst_2 : AddCommGroup V₂] [inst_3 : Module k V₁] [inst_4 : Module k V₂]
  [inst_5 : AddTorsor V₁ P₁] [inst_6 : AddTorsor V₂ P₂] (e : P₁ ≃ᵃ[k] P₂) (a b : P₁) (c : k),
  e ((AffineMap.lineMap a b) c) = (AffineMap.lineMap (e a) (e b)) c

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineEquiv

Cited by

5 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Quot.sound

Assumes

RingAddCommGroupAddCommGroupModuleModuleAddTorsorAddTorsor